MOLAP is a OLAP environment based on a MultiDimensional database (MDDB) such as TM1, Hyperion, and SSAS. ROLAP is an OLAP environment based on a relational database (RDB). MDDB's are physically different than RDB's. Whereas in a RDB data is stored in tables, rows and columns, in an MDDB, data is stored in cells within a cube. MDDB's provide significantly better performance but significantly lower capacity. They usually contain aggregate data and supported by detailed (atomic level) star schema implemented in a relational database.

To expand on the first reply, MOLAP/MDDB may appear to be faster, but it usually depends on when you start timing. If your existing cubes don't answer your question and new one(s) need to be built, add this time into the overall response time. And because of the indexing and physical storage of values for all the drill paths you may have requested, the overall size is significantly smaller than what a ROLAP tool can offer. Also, because the cube is a store of aggregated data, it's likely that you cannot drill directly into the underlying, causal atomic detail data.

Just an FYI on a few things:1) Yahoo have a 18Tb MOLAP SSAS cube. So there is no real size restriction on MOLAP cubes2) SSAS can do MOLAP, HOLAP and ROLAP. I work in a Teradata environment where we use SSAS and have MOLAP dimensions with ROLAP fact data.3) SSAS does not pre-aggregate data by default. However it is designed that it can still aggregate data quickly, and aggregations may be built on an SSAS cube (whether MOLAP or ROLAP).